Determination of the location of the flame front in a subterranean formation



July 23, 1957 R. JENKINS 2,300,133

DETERMINATION OF THE LOCATION OF THE FLAME FRONT IN A SUBTERRANEAN FORMATION Filed NOV. 9, 1953 zmmtwm dmiiim/ m ARODMAN JENKINS n tt i:

DETERMINATION OF THE LGATEN OF THE FLANIE FRQNT IN A SUBTERRANEAN FORMA- TION Rorlman Jenkins, Dallas, Tex., assignor, 32 ments, to Socony Mobil Oil Company, inc, a corporation of New York Application November 9, 1953, enial No. 391,065

6 Claims. (Cl. 1664) combustion supporting gas is injected into the formation.

through an input well and combustion of hydrocarbon within the formation is initiated by suitable means. The formation is provided with a single output Well, or is provided with four output wells, each of the four output wells spaced 90 from each other on a circle having the input well as its center, and, as the flow of combustion supporting gas to the formation is continued, a flame front migrates from the input Well to the output well or output wells. Combustion gases, oil, and distillation and viscosity breaking products of the hydrocarbon migrate in advance of the flame front to the output well or output wells from which they are removed to be treated for recovery of the desired valuable hydrocarbon material or other constituents. The heat of the fluids migrating in advance of the flame front strips the hydrocarbon-containing formation of water and the greater portion of the hydrocarbon leaving behind a carbonaceous deposit. This carbonaceous deposit is essentially the fuel consumed in the process and the flame front migrating from the input well to the output Well or wells is the zone of combustion progressively moving through the carbonaceous deposit. In carrying out the combustion process, it is often necessary or desirable to determine the location of the flame front with respect to its distance between the input well and the output well or one or more of the output wells. Thus, to estimate the yield of hydrocarbon materials, to estimate the time of arrival of the flame front at an output well, to control the rate of advance of the flame front, or to efiect other purposes, knowledge of the location of the flame front is essential.

It is the principal object of this invention to provide a method for determining the location of a flame front in a subterranean formation wherein combustion has been effected for the purpose of recovering hydrocarbon materials. Other objects of the invention will become apparent from the following detailed description thereof.

In accordance with the invention, there is provideda method for the location of the flame front in a subterranean formation between an input Well leading to the formation and an output'well leading from the formation which comprises as essential steps thereof the determination both prior and subsequent to the initiation of combustion within the formation of the time required for gas to travel through the formation between the input well and the output well and the determination of the porosity of the formation.

2,800,183 Patented July 23, 1%5'7 time required for a gas to travel through the formation between an input Well leading to the formation and an output well leading from the formation is dependent upon the gas saturation within the formation. By gas saturation is meant the fraction of the pore volume of the material of the formation which is occupied by gas. Passage of the flame front through the formation removes the carbonaceous deposit and since the heat of the fluids migrating in advance of the flame front strips the formation of the water and the greater portion of the hydrocarbons, the gas saturation in the portion of the formation traversed by the flame front is unity, i. e., the entire pore volume of the material of the formation is occupied by gas. Thus, the passage of the flame front through the formation changes the time required for a gas to travel through the formation between the input well and an output well, and from the change'in time the location of the flame front between the input well and the output well can be determined.

The gas saturation in a subterranean formation prior to passage of the flame front therethrough can be expressed as follows:

where S==the gas saturation, fraction of the pore volume of the t material of the formation occupied by gas Q=rate at which gas is injected into the formation through the input well, standard cubic feet per hour t=time required for gas to travel through the formation The time required for gas to travel through the formation between the input well and an output well, all other factors being equal, will be a function of the ratio of the pressure at which the gas is injected into the input well, Pw, and the-pressure at which the gas leaves the output well, P0. The time will also be a function of the output well pattern since the number of the output wells and their spatial positions with respect to the input well will govern the area of the formation swept by the gas traveling through the formation from the input well. This fac tor representing the ratio of the pressure at which the gas is injected into the input well and the pressure at which the gas leaves the output well and the output well pattern appears in the above equation as the dimensionless time factor 0. Its value for various ratios of the pressure at which the gas is injected into the input well and the pressure at which the gas leaves the output well prior to the initiation of combustion has been mathematically determined by me from basic equations of fluid flow in porous media and 'is given in the accompanying figure. In the figure, the abscissa is the ratio, Pw/Po, of the pressures and the ordinate is the dimensionless time factor, 0. Curve A gives the variation in the value of 0 with the variation in the value of Pw/Po for the case where the formation contains one output well, i. e., a two-well pattern, and curve B gives the same information for the case where the formation contains four output The invention is based upon the discovery that the wells spaced from each other on a circle having the input well as its center, i. e., a five-well pattern. From either curve A or 'B, depending upon the well pattern, the value of can be determined for each ratio Pw/Po of thepressures. The values of the ratio Pw/Po given in the figure are between 1 and 500 which includes all values ordinarily encountered in practice. For'higher values of the ratio Pw/Po greater than 500, the value of 0 may be taken as 0.113 for a two-well pattern and as 0.156 for a five-well pattern.

Subsequent to the initiation of combustion, the value of the dimensionless time factor, 0, is obtained from Equation 1 and is expressed as follows:

In Equation 2, the valueof S is the value prior toinitiation of combustion in the formation.

By the method of: the invention,'the.1ocation of the flame front along a straight line betweenthe inputwell and the output'well in'a two-'well-pattern'or any particular output well in a five-well. pattern canbe determined at any time during combustion within the formation. For this determination there .is.:measured,-.prior to initiation of.;combustion within the .formation, the time required by gas to travel through the formation :between the input well and the particular output well. Measurement of this time is effected by injecting into thefformation through the input well any gas whichis capable of traveling through the formation and from which a gas component is obtained whose arrival at the particular output well will be detectableand measuring the time between the entrance of the gas into the formation and the first appearance of the detectable gas component at the particular output well. This gas may be air or other combustion supporting gas to be employed for maintaining combustion within the formation, if its arrival at the output well is detectable, or this gas may be some gas other than the combustion supporting gas. The detectable gas component may be a component originally present in the gas or may be a component produced therefrom by reaction within the formation. The time may be conveniently measured, if detection of the arrival *at the particular output well of a detectable gas component obtained from the combustion supporting gas is difiicult or undesired, involves by a procedure which injecting into the formation the combustion supporting gas, adding to-the combustion supporting gas another gas which will accompany the combustion .supporting gas through the formation and from which agas component is obtained whose arrival at the particular output well is detectable, and measuring the time between the injection of .thisgas, hereinafter termed a tracergas, and the first appearance of the detectable gas component at the particular output well.

.Theqtirne, t, forgas to travel through the formation between the input well and the particular output Well having been measured, its value issubstituted in Equation 1. The rate at which the gas is injected into the formation through the input well and the pressures at the input well and the particular output well will be known or are readily measurable. These values are substituted in Equation 1 for Q, Pw, and P0, respectively. From the ratio Pw/Po, the value for 0 is obtained from the accompanying figure and this value is also substituted in the equation. Additionally, the distance between the input well and the particular output well, as well as the thickness of the formation, will be known or is readily measurable and these values of L and 'h., respectively, are substituted in the equation. The right hand side of Equation 1, therefore, will be complete except for the value of the porosity Knowing the porosity of the formation, the gas saturation may be calculated fromEquation ,1. It is true that knowing the gas saturation, the porosity may be calculated from Equation 1 and that both the porosity and the gas saturation may be measured .onacore sample taken from 7 the formation. However, since gas saturation is expressed as the fraction of the pore volume of the material of the formation occupied by gas, measurment of gas saturation also involves measurement of pore volume, or porosity. But of greater significance is the fact that the measurement of gas saturation of a core sample is unreliable because of difficulties in preventing loss of liquid from the core sample, contamination of the core sample with liquids Within the bore hole during the sampling operation, and loss of liquid from the core sample with change of pressure upon removal from the formation. Therefore, from the standpoint of accuracy the porosity of the core sample is measured. For the same reasons, the time required for gas to travel through the formation between the input well and the particular output well before combustion is initiated in the formation is measured, even though it could be calculated from Equation 1 by employing a measured value of the gas saturation and the measured value of the porosity.

The porosity of the core sample may be measured in any known manner. Suitably, the core sample after being cleaned and dried is placed in a chamber and subjected to a known pressure of a gas. The gas pressure is thereafter reduced a known amount and the volume of gas leaving the core sample as a result of the reduction in pressure is measured. Knowing the volume of gas leaving the pore spaces of the core sample and the reduction in pressure, the volume of the pore spaces, or the porosity,

can be calculated employing the gas law.

The value for each of the factors having been substituted in Equation 1, the value of S is then calculated. The value of S need be determined with respect to only one output well where a five-spot well pattern is employed. However, in order to minimize errors in determining the location of the flame front between the input well and. any of the other output wells arising from possible differences in the value of the gas saturation, it is preferred to determine the value of S with respect to each of the output wells.

Following determination of thegas saturation, initiation of combustion is effected within the formation. Thereafter, combustion supporting gas is injected into the formation to maintain the combustion and the flame front migrates into the formation from the input well. At any time subsequent to initiation of combustion within the formation, measurement of the time required for gas to travel through the formation between the input well and any outputwell will locate the position of the flame front on 'a straight line between the input well and the particular output well. Measurement of the time required 'for gas to travel through the formation between the input well and any output well subsequent to the initiation of combustion is effected by adding to the combustion supporting gas being injected into the input Well any gas which will accompany the combustion supporting gas through the formation and from which a gas component is obtained whose arrival at the output well will be detectable, i. e., a tracer gas, and measuring the time between the entrance of this gas into the formation and the first appearance of the detectable gas component at the output well. The detectable gas component may be, as before, a component present in the gas injected into the input well or may be a component produced therefrom by reaction within the formation.

Helium is preferred as the tracer gas. However, radon or neon may be employed. The tracer gas added to the combustion supporting gas subsequent to initiation of combustion may be the same or may be a different tracer gas than the one employed, if such is the case, prior to initiation of combustion within the formation.

Addition of the tracer gas to the combustion supporting gas, either prior or subsequent to the initiation of combustion, may be accomplished by any suitable means. For example, the tracer gas may be admixed with combustionrsupporting gas in .a tank, a 'pressure may be. im-

posed on'the mixed gas in the tank above the pressure at which combustion supporting gas is being injected into the formation, and the mixed gas may be bled into the stream of combustion supporting gas. The rate at which the mixed gas is bled into the stream of combustion supporting gas may vary and will depend upon the concentration of tracer gas in the mixed gas and the rate of flow of the combustion supporting gas. 7 Generally, the tracer gas may be admixed in the tank with the combustion supporting gas in a volume ratio of about 1 to 10 and the rate at which the mixed gas is added to the stream of combustion supporting, gas should be suchthat the concentration of the detectable gas component in the mixture entering the input well will be sufiiciently high to render the component readily detectable when arriving at the output well. The addition of about one standard cubic foot of tracer gas in admixture with about ten standard cubic feet of combustion supporting gas to the stream of combustion supporting gas over a period of about 30 seconds has been found to be satisfactory.

Detection of the appearance of the detectable gas component at the output well for the purpose of determining the time required for travel of gas through the formation may be made by any suitable procedure dependingupon the detectable gas component. Where helium is employed, the detectable gas component will be helium and periodic analysis of the gas entering the output well for the presence of the added helium may be made. A suitable analytical procedure for helium comprises taking at short time intervals samples of the gas entering the output well from the formation, the time of taking each sample being noted, and contacting the samples with charcoal at liquid nitrogen temperatures whereby all gas except helium is absorbed, and noting the volume of unabsorbed gases. The presence of a volume of unabsorbed gas in any sample greater than the volume of helium that would be expected from the quantity naturally present in the combustion supporting gas indicates the presence of the added helium. Analysis for neon at the output well, where neon is used as the tracer gas, may be similarly made. Where radon is employed, radon will be the detectable gas component and its presence in the gas entering the output well may be determined by measurement of the radioactivity of this gas, a Geiger-Mueller counter, a scintillation counter, a proportional counter, or other type of radioactivity measuring instrument being employed for this purpose. Knowing the time the tracer gas enters the formation through the input well and knowing the time that the detectable gas component enters the output well from the formation, a value of t subsequent to initiation of combustion becomes known.

The values for Q, Pw, and P are also determined. During the measurement of the time, t, for gas to travel through the formation between the input well and the output well, it is contemplated that the values for Q, Pw, and Po shall remain substantially constant. However, variations in these values during the measurement of the time, t, may occur. In such cases, the values for Q, Pw, and P0 to be employed in the equations should be integrated values taken over the period of time required by the gas to travel between the input well and the outputwell.

The location of the flame front on a straight line between the input well and the particular output well is given by the following equation:

FFL=g S (3) where FFL=the flame front location expressed as the fraction of the total distance on a straight linefrom the lnput .well to the particular output well 0,=: the dimensionless time parameter employed inEquadeal for determining S and obtained from thefigure for the ratio of \PW/PO employed prior to initiation of combustion 0,=the dimensionless time parameter given by Equation 2, and

S=the gas saturation of the formation prior to initiation of combustion as determined from Equation 1 The value of 0, and S being known, the location of the flame front is determinable from Equation 3 upon determining 0,. This latter value is obtained from Equation 2 employing therein the same values for 0, h, and L employed in Equation 1 for determining the value of S and the values for Q, Pw, Po, and t as determined subsequent to the initiation of combustion. The value of 0, being known, this value is substituted in Equation 3 whereby the location of the flame front becomes known.

The following example will be illustrative of the .invention.

An input well and four output wells spaced from each other on a circle having theinput well as its center, i; e., a five-spot well pattern, were drilled into a petroleum oil formation. Each output well was at a distance of feet from the input well. By logging methods employed in the input well and the output wells, the average thickness of the formation was determined to be 20 feet and from core samples taken during drilling of the wells, the porosity of the material of the formation was determined to be 0.3. Air was injected into the formation through the input well at a constant rate of 10,000 standard cubic feet per hour and the pressure at the input Well Was 600 pounds per square inch. Pressure at each of the output wells gradually increased but eventually stabilized. At one of the output wells, identified as well No. l, the pressure stabilized at 100 pounds per square inch. While air was being injected into the input Well, the rate and pressure at the input well and the pressure at the output well being as stated, helium was added to the air by admixing one cubic foot of helium with nine cubic feet of air in a tank, pressuring to approximately 650 pounds per square inch, and bleeding within onehalf minute the mixed gas from the tank into the air stream entering the formation. Samples of the gas leaving the formation at well No. 1 were thereafter taken at intervals of 15 minutes, the time of taking each sample being noted, and the samples were analyzed for helium by contacting with charcoal held in a chamber provided with a jacket through which liquid nitrogen was circulated. Added helium appeared in the sample taken 20 hours after the helium and air mixture was bled into the injected air stream. The value of t was, accordingly, 20 hours. From the ratio of the pressures at the input well to the pressure at well No. 1, the value of 0.145 was taken from curve B of the figure. The values for Q, t, (p, h, L, Pw, Po, and 0 were substituted in Equation 1 as follows:

of addition and the amount of helium 'being the same as described above. The pressure at the input well was 400 pounds per square inch at the time of the addition of the helium. The pressure at well No. 1 was 100 pounds per square inch and the rate of injection of air was 10,000 standard cubic feet per hour. Samples were thereafter taken of the gas leaving well No. 1 and were analyzed for helium, the analysis procedure being the same as described above. The time of taking each sample was noted and 70 hours after addition of the helium to the air injected into the input well, added helium appearediinzthe gas leavingthezoutput well. TEhe value ;of t; was, accordingly, 70 hours. The values for Q,.:t, 11, L,::P.w, Po, and ,-S;'b.eingl nown,: the valuefor fl iwas calculated from Equation 2 as follows:

The value of .0 was,:accordingly, 0.711. The values of, 6 and S were-substituted in Equation 3 asfollows:

EFL-1 0768 andthetvalue of FFLwasthus 0.376. The name front accordingly was located.:at adistance from the input well .along ea straight line .:between the .input well and well 'No. .1 equal ;to,v0.3 7-6 -of thetotal'distance, along a straight line between these two wells.

The inventionmay be employediinconnection with the .combustion :process lforntherecoveryzof petroleum oil from partially depleted subterraneanpetroleum,oil reservoirs .where the reservoir .energy .has decreased to the point thatoil is no longer naturally forced to the surface and=.particularly.to the point that; the rate of recovery by pumping isirsolow has to be uneconomical. The inventionrnay .also behemployed in connection with the combustion process for the recovery .of petroleum oil from a subterranean reservoir wherein the oil .has such high viscosity that efiicientrecovery by water drive or other conventional:means cannot be effected. Further, the invention is :applicable in connection with the combustion process for the recovery of hydrocarbon materials from earth formationssuch as/tar sands, ,for example, those existing in the Athabasca region of Canada and elsewhere.

Havingthus described my invention, it will be understood that such description has been given by way of illustration. and example and not by way of limitation, reference for the latter purpose being had to the appended claims.

I: claim:

1. :In the process for the recovery of .hydrocarbon materials from a subterranean formation .containing hydrocarbons and havingan input well leading thereto andHatLleast: one output well leading therefrom by combustion within said subterranean formation wherein a flame front travels throughtsaid subterranean formation from said input'well .to said output well, the steps comprising measuring 'the'distance between saidinput well and said out-put well and thethickness of said subterranean formation, determining the porosity of said su'bterranean formation, determining prior to initiation .of combustion Within said subterraneanformation the gas saturation of saidtsubterranean formation, passing gas priortto initiation of combustion withinsaid subterranean formation throughsaid subterranean formation between said input well and said output well at a known 'gaspressure at said input well and at said output well whereby the value of a first dimensionless time factor related to the pressure atwhich said gas is injected into said input well and the pressure at which gas reaches said output well may be taken from the accompanying .figure, initiating combustion within said subterranean formation, supplying combustion supportinggas to saidisubterranean formation through said input well, and measuring eat a time subsequent to initiation of combustion .in :and following supplying of combustion supporting .gas to said subterranean formation the time required for .gas to'travel through saidsubterranean formationbetween said input well-and said output well at a known rate of injection of said gas into said input well andat aknown gasipressure at said input well andvat said output iwell where'byia second 'climensionless time factor :0 may be determined from the equation:

in which equation .8 is ithe igas :saturatiornofsaidssub terranean formation prior to initiation :of -combustion expressed as the fraction'of the; pore volum-eof-thegmate;

rial lof said subterranean formation occupied .;by-gas;

Q vis the rate at which-said gasis injectedinto said;sub-, terranean formation through said input a well i expressed as standard cubic; feet per hour; 2 is the .time :required for-said gasto travel through-said subterranean formation fromasaidinputvvell to said outputjwell expressed as hours; istheqporosity of said subterranean formation expressed as the fraction of the. bulk volume of the material of said subterranean formation .occupiedbypore space; -h is the thickness of said subterranean formationexpressed :as -feet;, .L.is the distance betweensaid input wellrandsaid output well expressed as "feet; Pw is the;

pressure at which said gas is injected into saidinput well expressedas pounds per square inch; P0 is the pressure at which said gas reaches the output-well expressed in poundsper square inch; and whereby the location of the flame ,front within said's ubterranean formation may be determined from the equation:

in *which'equation FFL is the location of the flame front expressed as the fraction of the distance between-the in- 1 put well-and the output-well; -9 is said first dimensionless timefactor; 0 is' said-second dimensionless time factor;

and-S is the-gas saturation of s'aidsubterranean formationprior to initiation of combustion expressed as the fraction of thepore volume of the material of said subtion for gas to travel through said subterraneanforma tionflbetween said input well and said output well at a known rate of injection of said gas into said input well and at a known gas pressure at said input well and .at' said-output well, (b) is the gas saturation insaidrsubten' ranean formation prior to initiation of combustion within said subterranean formation, and. (c) is the porosity of said subterranean formation, whereby the third termmay be determined from the equation:

in which equation S is the .gas saturation expressed as the fraction of the pore volume of the material of said subterranean formation occupied by gas; Q is the rate at which .gas is injected into saidsubterranean formation through the input well expressed as standard cubic feet per hour; 2 is the time required for gas to travel through said subterranean formation between the input-well and the output well expressed as hours; is the porosity of saidasubterranean formation expressed as the fraction'of thexbulk volume of the material of said subterranean formation occupied by pore space; h is the thickness of said subterranean formation expressed as feet; L is the distance between the input well and the output well expressed as feet; Pw is the pressure at which the gas is injected into the input well expressed as pounds per square inch; P0 is tthe pressureuat which the gas reaches the out:

puttwell-expressedin pounds ,per square inch; and dis a dimensionless time factor related to ,Pw and Po and'the wellpattern and has a value taken from the accompanyingfii -gure; initiating combustion within said subterranean 9 formation, supplying combustion supporting gas to said subterranean formation through said input well, and measuring at .a time subsequent to initiation of combustion in and following supplying of combustion supporting gas to said subterranean formation the time required for, gas to travel through said subterranean formation between said input well and said output well at a known rate of injection of said gas into said input well and at a known gas pressure at said input well and at said output well, whereby the term may be determined from the equation:

2.339Qt, 2) Pw+P.,

in which equation each term has the definition as in Equation 1 and S has the same value as in Equation 1, and the location of the flame frontwithin said subterranean formation may be determined from the equation:

Equation 1; 6 has the value of O'in Equation 2; "and S- has the value of S in Equations 1 and 2.

3. In the process for the recovery of hydrocarbon materials from a subterranean formation containing hydrocarbons and having an input well leading thereto and at least one output well leading therefrom by combustion within said subterranean formation wherein a flame, front travels through said subterranean formation from said input well to said output well, the steps comprising measuring the distance between said input well and said output well, the thickness of said subterranean formation, and the porosity of said subterranean formation, measuring prior to initiation of combustion within said subterranean formation one of two terms (a) and, (b), of which two terms (a) is the time required for gas to travel through said subterranean formation between said input well and said output well at a known rate of injection of said gas into said input well and at a known gas pressure at said input well and at said output well, and (b) is the gas saturation in said subterranean formation whereby the second term may be determined from the equation:

the bulk volume of the material of said subterranean. formation occupied by pore space; h is the thickness of,

said subterranean formation expressed as feet; L is the distance between the input well and the output well expressed as feet; Pw is the pressure at which the gas is in jected into the input Well expressed as pounds per square inch; P0 is the pressure at which the gas reaches the output well expressed in pounds per square inch; and- 0 is a dimensionless time factor related to Pw and P0 and the well pattern and has a value taken from thetaccompanying figure; initiating combustion within said subterranean formation, supplying combustion supporting gas to said subterranean formation through said input well, and measuring atva time subsequent to initiation of combustion in and following supplying of combustion supporting gas to said subterranean formation the time required for gas to travel through said subterranean formation between said input well and said output well at a known rate of injection of said gas into said input r 10 well and at a known gas pressure at said input well and at said output well, whereby the term 0 may be determined from the equation:

2.33am w+ a) in which equation each term has the definition as in Equation 1 and S has the same value as in Equation 1,

and the location of the flame front within said subterranean formation may be determined from the equation:

in which equation FFL is the location of the flame front expressed as the fraction of the distance betweenjthe input well and the output well; 0, has the value of 0 in Equation 1; 0 has the value of 0 in Equation 2; and S has the value of S in Equations 1 and 2.

4. In the process for the recovery of hydrocarbon materials from a subterranean formation containing hydrocarbons and having an input well leading thereto and at least one output well leading therefrom by combustion within said'subterranean formation wherein a flame front travels through said subterranean formation from said FFL=%S input well to said output well, the steps comprising measuring the distance between said input Well and said,

in which equation S is the gas saturation expressed as the fraction of the pore volume of the material of said subterranean formation occupied by gas; Q is the rate at which gas is injected into said subterranean formation through the input well expressed as standard cubic feet per hour; if is the time required for gas to travel through said subterranean formation between the input well and the output well expressed as hours; 41 is the porosity of said subterranean formation expressed as the fraction of the bulk volume of the material of said subterranean formation occupied by pore space; h is the thickness of said subterranean formationexpressed as feet; L is the distance between the input well and the output well expressed as feet; Pw is the pressure at. which the gas is injected into the input well expressed as pounds per square inch; P0 is the pressure at which the gas reaches the output well expressed in pounds per square inch; and His a dimensionless time factor related to Pw and Po and the well pattern and has a value taken from the accompanying figure; initiating combustion within said sub terranean formation, supplying combustion supporting gas to said subterranean formation through said input well,

and measuring at a time subsequent to initiation of comin which equation, each term hasfthe definition as in. Equation 1 and S'hasrthesame value as in Equation 1,;

andihelocatiomof; the flamefront within said subtere ranean-iformationimay. bedetermined-from the-equation:

in which equation FFL is'the location of the flame front expressed as the fraction of the. distance. between the.

FFL=QS input well and the output well; li has thevalue ofyfl in Equation 1; 02 has the value of; in Equation 2; and-S, has .the value of- S in Equations 1, and 2.7

5. In the process for the recovery of hydrocarbon materials from a subterranean, formation containing hydrocarbons and having an input well leading thereto and only one output wellleading therefrom by. combustion.

within said subterranean formationwherein a flamev front travels through said subterranean formation from said inputtwell to saidoutput well, the steps comprising measuring the distance between said input well and said output well, thethickness of said subterranean formation, and the porosity of said subterranean formation, measuring prior to initiation of combustion withinsaid subterranean.

formation the time required for gas. to travel through said subterranean formation between said input well and said output well at a known rate of injection of. said gas into saidiinput well and at a knOWn gas pressure at said,

input well and at said output well whereby the gas saturation in said subterranean formation may bedeterrnined from the equation:

the bulk volume of the material of said subterranean,

formation occupied by pore space; h is the thickness of said subterranean formation expressed as feet; L is the distance between the input well and the outputwell expressed as, feet; P'w is the pressure at which the gas is injected into the input well expressed as pounds per square inch; P0 is the pressure at which the gas reaches the output well expressed in pounds per square inch; and

0 is a dimensionless time factor'related to Pw and Pa and.

has a value taken from the curve A in the accompanying figure; initiating combustion within said subterranean formation, supplying combustion supporting gas to said subterranean formation through said input well, and measuring at a time subsequent to initiation of combustion in and following supplying of combustion supporting gas to said subterranean formation the time required for gas to travel through said subterranean formation between said input well and said output well at a known rate of injection of said gas into said input well and at Ya known gas pressure at said input well and at said output well, whereby the term 0 may be determined from the equation:

in which equation each term has the definition as in Equation 1 and S has the same value as in Equation 1,

and the location of the flame front within said subter ranean formation may be determined from the equation:

FFL S Equation 1; fl vhas the value of a in Equation 2; and S 7 has the value of S in Equations 1 and 2.

1 reaches saidone of said output wells expressedin pounds 6, Inthe process for the. recovery ofhydrocarbon ma-.

terials from a, subterranean formationcontaining hydrocarbons and having an input well leading thereto and four outputwellsleading therefrorn, said output wells being sp aced v fromeachgother on.a circle having, the input welljas itscenter, by; combustion ,withinsaid subterranean formation whereina flame front travels through said subterranean formation from; said input well to one of said output wells, the steps, comprising measuring the 1 distance betweensaidinput;well and said one of-- said output wells, the thickness of said subterranean forrna-.

tion, and the porosity of said. subterranean formation, measuring prior to initiation of combustion within said subterranean formation the time required for gas to travel through said" subterranean formation between said input Well and said one of said output wellsata known rate of injection of said gas into said input well and at a known gaspressure atsaid input well and at said one of said output wells whereby the gas saturation in said subterranean formation may be determined from the equation:

1 said subterranean formation between the input well and said one of said output wells expressedas hours; is the porosity of said'subterranean formation. expressed as the fraction of the bulk volume of the material of said subterranean formation occupied by pore space; It isthe thicki ness of said subterranean formation expressed as feet; L

is the distance between the input well and said one of said output wells expressed as feet; Pw is the pressure at which the gas is injected into the input well expressed as pounds per square inch; P0 is the pressure at which the gas per square inch; and 6 is a dimensionless time factor related to Pw and Po and has a value taken from the curve B in theaccompanying figure; initiating combustion within said subterraneanformation, supplying combustion supporting gas to said subterranean formation through said input well, and measuring at a time subsequent to initiation of combustion in and following supplying of combustion, supporting gas to said subterranean formation the time required for gas to travel through said subterranean formation between saidinput wellv and said one of said output wells at a known rate of: injection of said gas into said input well and ata known gaspressure at said input well and at said one of said output wells, whereby the term 6 may be, determined from the equation:

in which equation each term has the definition as in Equation 1 and S has the same value as in Equation 1, and the location of theflame front within said subterranean formation may be determined from the equation:

(3) FFL= s in which equation FFL is the location of the flame front expressed as the fraction of the distance between the input well and said one of said output wells; 6 has the value of 0 in Equation 1; 0 has the value of 0 in Equation 2; and S'has the value of S in Equations 1 and 2.

References Cited in the file of this patent STATES PATENTS 2,390,770. Barton et a1. Dec. 11, 1945 2,578,500 Bernard et a1. Dec. 11,- 1951 2,642,943 Smithet-al. June 23, 1953 

1. IN THE PROCESS FOR THE RECOVERY OF HYDROCARBON MATERIALS FROM A SUBTERRANEAN FORMATION CONTAINING HYDROCARBOSN AND HAVING AN IMPUT WELL LEADING THERETO AND AT LEAST ONR OUTPUT WELL LEADING THEREFROM BY COMBUSTION WITHIN SAID SUBTERRANEAN FORMATION WHEREIN FLAME FRONT TRAVELS THROUGH SAID SUBTERRABEAB FORMATION FLAME FROM TRAVELS THROUGH SAID SUBTERRANEAN FORMATION FROM SAID INPUT WELL TO SAID OUTPUT WELL, THE STEPS COMAND SAID OUTPUT WELL AND THE THICKNESS OF SAID SUBTERRANEAN FORMATION, DETERMINING THE POROSITY OF SAID SUBTERRANEAN FORMATION, DETERMINING PRIOR TO INITIATION OF COMBUSTION WITHIN SAID SUBTERRANEAN FORMATION, PASSING GAS SATURATION OF SAID SUBTERRANEAN FORMATION, PASSING GAS PRIOR TO INITIATION OF COMBUSTION EITHIN SAID SUBTERRANEAN FORMATION THROUGH SAID SUBTERRANEAN FORMATION BETWEEN SAID INPUT WELL SAID AND AT A KNOWN GAS PRESSURE AT SAID INPUT WELL AND AT SAID OUTPUT WELL WHEREBY THE VALUE OF A FIRST DIMENSIONLESS TIME FACTOR O RELATED TO THE PRESSURE AT WHICH GAS REACHES SAID OUTPUT WELL AND THE PRESSURE AT WHICH GAS REACHES SAID OUTPUT WELL MAY BE TAKEN FROM THE ACCOMPNYING FIGURE, INITIATING COMBUSTION WITHIN SAID SUBTERRANEAN FORMATION, SUPPLYING COMBUSTION SUPPORTING GAS TO SAID SUBTERRANEAN FORMA- 2.339QT $= $HL2(P+P)S 